The present invention rolates to methods and apparatus for logging earth formations penetrated by a well borehole, and more particularly to improved methods and apparatus for determining formation characteristics by the analysis of the formation conductivity.
The clay counter-ion concentration is well recognized as an important factor in the interpretation of the resistivity of shaly sands. See, for example, Waxman, M. H. and Smits, L. J. M. "Electrical Conductivities in Oil-Bearing Shaly Sands". Soc. Pet. Eng. J. (June, 1968), presented as Paper (SPE 1863-A) at SPE 42nd Annual Fall Meeting, Houston, Tex., Oct. 1-4, 1967; and Clavier, C., Coates, G., and Dumanoir, J. "The Theoretical and Experimental Bases for the `Dual Water` Model for the Interpretation of Shaly Sands", Soc. Pet. Eng. J. (October 1977), presented as Paper (SPE 6859) at SPE 52nd Annual Fall Meeting, Denver, Colo. Oct. 9-12, 1977. As explained therein, because the clay counter-ions aug-ment or supplement the conductivity of the formation water, it is necessary to correct electrical formation measurements for the added clay counter-ion conductivity. Such corrections prevent overestimation of the formation fractional water saturation S.sub.w.
As presently understood, the counter-ion conductivity provided by such clay mineral classes as illite, kaolinite, and smectites results from large insoluble anions which are captive in the clay particles, and whose negative charges are counterbalanced by soluble mobile cations (which are the counter-ions). ("Large" in this context is with respect to the size of the mobile cation, although a clay mineral particle size of 2 microns would also be small relative to the normal grain size.) The negative charges in the clay are believed to occur from substitution of bi-valent atoms (e.g., Mg or Fe) for tri-valent Al in the clay lattice, or from cyrstal defects in the clay lattice. This creates a local electrical unbalance which is compensated by positive ions, or counter-ions, at the surface of the clay. The resulting positive surface charge is called the clay cation exchange capacity (CEC). The CEC is expressed on a weight basis in milliequivalent (meq) per 100 grams of dry material.
The well recognized Waxman-Smits (W-S) model (see above references) for rock conductivity may be expressed as: EQU C.sub.t =.phi..sup.m S.sub.w.sup.n (C.sub.w +BQ.sub.v) (1)
where:
.phi..sup.m and S.sub.w.sup.n have their usual Archie relationship meaning, PA1 C.sub.t is the true conductivity of the formation, PA1 C.sub.w is the conductivity of producible pore water, PA1 B is the counter-ion mobility, and PA1 Q.sub.v is the counter-ion concentration (CEC) ##EQU1## Pg=matrix density. The BQ.sub.v term is the conductivity added to the system by the clay. From this expression the need to correct the electrical measurements for added clay counter-ion conductivity is self-evident.
Various methods are known for determining the term Q.sub.v, such as correlation with classical shale indicators. Clavier, Coates, and Dumanoir (supra) state that gamma ray and SP logs have been found especially useful for estimating Q.sub.v, and mention one study which found a strong correlation between gamma-ray count rate/.phi..sub.t and Q.sub.v (see FIG. 2 of the present invention disclosure).
Clays are hydrous alumino-silicate sheet minerals. Illite is the only one which incorporates potassium in its structure. The other naturally radioactive elements (uranium and thorium) are associated in some other way with clays and shales, but potassium does not constitute a part thereof. In fact, since potassium can be present in the rock matrix itself (as distinguished from the clays and shales), in the form of feldspar and mica, for example, excessive clay may be indicated if radiation from potassium is considered. Alternatively, some clays (kaolinite, for example) can be terribly deficient in potassium, leading to errors in the opposite direction. In short, as now recognized and taught herein, potassium can be dangerous to use as a Q.sub.v indicator.
A need therefore remains for a method and apparatus which will provide for determining the clay counter-ion concentration in a fluid bearing shaly sand formation, preferably by measuring the formation natural gamma-ray radiation without being affected by perturbations introduced by unrelated variations in the potassium content of the clays, shales, and other formation constitutents. The method and apparatus should furnish such measurements in an inexpensive, uncomplicated, durable, versatile, and reliable method and apparatus, which are inexpensive to manufacture and utilize, and readily suited to the widest possible utilization in logging earth formations penetrated by a well borehole, to determine the formation characteristics.